algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
The conformal bootstrap program (Belavin-Polyakov-Zamolofchikov 84) is an attempt to construct and classify conformal field theories non-perturbatively by axiomatizing the properties of their operator product expansion/correlation functions.
The conformal bootstrap was proposed in the 1970s as a strategy for calculating the properties of second-order phase transitions. After spectacular success elucidating two-dimensional systems, little progress was made on systems in higher dimensions until a recent renaissance beginning in 2008 (Poland-Simmons-Duffin 16).
The generalization of the conformal bootstrap to superconformal field theories has the potential to provide, via AdS/CFT, a precise and detailed construction of large-N and asymptotically AdS string/M-theory.
Alexander Belavin, Alexander Polyakov, Alexander Zamolodchikov, (1984). Infinite conformal symmetry in two-dimensional quantum field theory. Nuclear Physics B. 241 (2): 333–380 (1984)
David Poland, David Simmons-Duffin, The conformal bootstrap, Nature Physics 535–539 (2016) doi:10.1038/nphys3761
David Simmons-Duffin, TASI Lectures on the Conformal Bootstrap (arXiv:1602.07982)
David Poland, Slava Rychkov, Alessandro Vichi, The Conformal Bootstrap: Numerical Techniques and Applications, Rev. Mod. Phys. 91, 15002 (2019) (arXiv:1805.04405)
Shai Chester, Weizmann Lectures on the Numerical Conformal Bootstrap (arXiv:1907.05147)
Johan Henriksson, Analytic Bootstrap for Perturbative Conformal Field Theories (arXiv:2008.12600)
Pedro Liendo, Zhengwen Liu, Junchen Rong, The old conformal bootstrap revisited (arXiv:2108.07295)
See also:
Wikipedia, Conformal bootstrap
Zechuan Zheng, Bootstrap Method in Theoretical Physics [arXiv:2401.00350]
For gauge theories:
For Liouville theory:
Comparison to experiment – superfluid-transition:
Shai Chester, Walter Landry, Junyu Liu, David Poland, David Simmons-Duffin, Ning Su, Alessandro Vichi, Carving out OPE space and precise $O(2)$ model critical exponents, JHEP 06 (2020) 142 (arXiv:1912.03324)
exposition in:
Slava Rychkov, Conformal bootstrap and the $\lambda$-point specific heat experimental anomaly, Journal Club for Condensed Matter Physics recommendation 2020 (pdf, doi:10.36471/JCCM_January_2020_02)
Solving the bootstrap constraints via machine learning:
Relation to reflection positivity:
For superconformal field theory, such as D=4 N=1 SYM, D=4 N=2 SYM, D=4 N=4 SYM, D=6 N=(1,0) SCFT, D=6 N=(2,0) SCFT:
Christopher Beem, Madalena Lemos, Pedro Liendo, Leonardo Rastelli, Balt C. van Rees, The $N=2$ superconformal bootstrap (arXiv:1412.7541)
Christopher Beem, Madalena Lemos, Leonardo Rastelli, Balt C. van Rees, The $(2,0)$ superconformal bootstrap (arXiv:1507.05637)
Christopher Beem, Leonardo Rastelli, Balt C. van Rees, More $N=4$ superconformal bootstrap (arXiv:1612.02363)
Luis F. Alday, Shai M. Chester, Pure anti-de Sitter supergravity and the conformal bootstrap [arXiv:2207.05085]
Discussion of superconformal bootstrap in view of AdS/CFT, hence as a precise and detailed construction of large-N but also small N and asymptotically AdS string theory/M-theory:
string scattering amplitudes :
Discussion of small N effects in M-theory using the conformal bootstrap:
Nathan B. Agmon, Shai Chester, Silviu S. Pufu, Solving M-theory with the Conformal Bootstrap, JHEP 06 (2018) 159 (arXiv:1711.07343)
Shai Chester, Bootstrapping M-theory, 2018 (pdf)
Specifically for the D=6 N=(2,0) SCFT on the M5-brane via AdS7/CFT6:
Shai Chester, Eric Perlmutter, M-Theory Reconstruction from $(2,0)$ CFT and the Chiral Algebra Conjecture, J. High Energ. Phys. (2018) 2018: 116 (arXiv:1805.00892)
from p. 2:
On the other hand, given our utter lack of a complete description of M-theory, the bulk is not terribly useful for determining finite aspects of the dual CFT. However, we can turn this problem around using the modern perspective of the conformal bootstrap, which gives an a priori independent formulation of the (local sector of the) CFT. This provides an independent tool for constructing M-theory at the non-perturbative level, a philosophy that we will substantiate in this work.
Luis Alday, Shai Chester, Himanshu Raj, 6d $(2,0)$ and M-theory at 1-loop, Journal of High Energy Physics 2021 133 (2021) [arXiv:2005.07175]
Specifically for the D=3 SCFT (BLG-model, ABJM model) on the M2-brane via AdS4/CFT3
Nathan B. Agmon, Shai Chester, Silviu S. Pufu, The M-theory Archipelago (arXiv:1907.13222)
Damon J. Binder, Shai Chester, Max Jerdee, Silviu S. Pufu, The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes (arXiv:2011.05728)
Last revised on January 2, 2024 at 19:27:18. See the history of this page for a list of all contributions to it.